318 



DISCUSSION OF THE SECULAR VARIATION 



Range of variability in tlie secular variation of the annual temperature. — If we 

 consider the deviations of the annual means from the normal temperature of the 

 place as fortuitous, we may employ a simple formula for the mean deviation as a 

 measure of the amount of variability, and deduce also a value for the prolable 

 uncertainty to which the normal temperature, or the mean of the whole series, may 

 be liable. 



Let e = the mean deviation of any yearly value, 



A = the difference of any annual mean from the normal temperature, 

 2A = their sum, irrespective of sign, 

 « = number of yearly values, 



then, with sufficient precision for our comparison, 



f = ± 1.253 ^, 



n 



which expression supposes the positive and negative A's to balance. The probable 

 uncertainty attaching to the mean of the series is given by 



2A 



±0.845 



n -y^ri 



Applying these expressions to a few of our larger and systematic series, we 

 deduce the following results : — 



Brunswick, Me.' 

 Salem, Mass. 

 New Bedford, Mass. 

 New Haven, Conn. 

 Marietta, Ohio . . 

 Fort Snelling, Minn, 

 Fort Leavenworth, Kan 

 Fort Brooke, Fla. . . 



Normal 

 T 



43-9 



49.0 



52-4 

 44.1 



52-7 

 71.7 



49 

 43 

 S8 



42 

 40 



27 



;l°.7S 

 1.48 



1-15 



1.25 

 1.24 

 2.07 

 1.83 

 1. 21 



.09 

 .12 



.16 



Lowest and 



HiMicst value 



Difference 

 from normal. 



1 +3-8 

 (-3-6 



1+2.2 



f— 3-3 



1+2-7 



1-3.8 



1+2.8 



1-2.7 



1+3.0 



f — 2.8 



1+4.2 



f — 4.0 



(+3.9 



f_i.6 



1+2.7 



Range. 



7-4 



iial means for 1S37— S— 9-40 are omitted, as defective. 



The weighted average value of the mean annual direction s is dz 1°.44, hence 



means derived from series of 25, 50, and 100 years are uncertain by a probable 



0.6745 e , , 



amount of r^ = j= — = ±0°.19, ±0°.14, and ±0°.10 respectively. To these 



values any errors that may exist in the graduation of the instruments would have 

 to be added. 



